Forces in Practice
Motion and Speed
Power and Work

Other Section


Speed and Motion

Speed or Velocity?

It is very important to understand the difference between these terms because Physicists are very fussy about the precise definition of words.

Speed is the rate of movement. Speed = distance / time

Velocity is not just the rate of movement, but the rate of movement in a certain direction. Velocity = displacement / time. The diagram below shows displacement. See how it can have positive and negative values.

diagram showing what displacement is


Acceleration is when the speed of an object is increasing. Like when you put up your speed when on the motorway. It does not go straight to 130km/h, but must speed up to reach it. The equation for acceleration is.

equation of acceleration

Speed - Time Graph

a speed time graph

From the start to point A the train is travelling at a constant speed of 10ms-1

Between points A and B it is accelerating because the line goes up, on a distance time graph this would appear as a curve. It accelerates at:
a = (v-u)/t
a = (30 - 10)/100
a = 0.2ms-2

From B to C it is at a constant speed of 30ms-1

To find the distance you calculate the area under the line using simple laws of geometry.

The main difference with a velocity / time graph is that when the line goes down it may mean the object is decelerating or it is moving in the opposite direction, so it is possible to have a negative velocity.

Stopping Distance

Stopping distance is the distance a vehicle travels from the point the driver should stop, to when he or she actually becomes stationary. It combines thinking distance and deceleration distance.
Here it is represented in a speed/time graph

graph showing stopping distance

Factors which can increase stopping distance are:

  • Speed. A faster vehicle will travel more distance (d = s x t).
  • Mass. A heavier vehicle may travel further because it has greater momentum.
  • Road condition. If the road is wet, for exaple, the vehicle will move more because there is less friction to stop it. That is why we should drive slower when it rains, the DSA advises that stopping distance is doubled in the rain and increases by 10 times on icy roads.
  • Reaction time. The thinking distance will be lengthened if the driver isn't concentrating or their reaction has been inhibited by alcohol or sleep deprivation for example.